SUCCESS!
Ordered a 629 Cylinder Stop (used I assume) from Jack First. It was much larger than the one on my 1917, but worked fine. I'd imagine that the old stop was either worked on or severely worn. So, when I put it in the gun, I noticed that there was a shoulder on the spring plunger that kept it from engaging in the hole on the new style stop.
First step was to plug the hole. I took a drywall screw (it's not your gun, be quiet!) and cut down the shaft so that it was about 3/8" long. I then epoxied the pin into the hole and contoured the outside to roughly the same proportions as the old stop. Worked great, but the larger stop created a timing problem. I adjusted timing by trimming down the stop engagement surface slightly and all was well.
Next step was to fix the trigger pull. Looks like some monkey had tried to give the gun a 'trigger job' and had nearly eliminated the single-action notch. I recreated the notch so that it was safe and then stoned it so it was smooth. Got the angles right, first try. Eat your heart out, John Browning! It helped that I had the sideplate off my 629 to compare.
Final analysis? Single action pull is fine, double action is still a bit weird with a hitch. There is not enough metal left to safely work the double-action pull so I'm leaving it rather than creating another problem. Cylinder times perfectly and there is minimal movement when locked.
One more step... I'm buying a set of Pachmayr Presentation grips that enclose the entire frame. It will hide some serious pitting and makes the gun feel good. I've got 17 half-moon clips left from the 1917 that got stolen. I'm sure I've got a few more and maybe a full moon clip or two, but it's time for a range trip now!